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4 years ago

Solve each equation and check to make sure both solutions work 2|5x-3|+10=4

Mathematics

1 answer:

Ede4ka [16]4 years ago

7 0

If your just looking for x then x=2

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Find a positive number for which the sum of it and its reciprocal is the smallest (least) possible. Let x be the number and let

Allisa [31]

Answer:

$S(x) = x + \frac{1}{x}$ --- Objective function

Interval = $\{x:x=1\}$

Step-by-step explanation:

Given

Represent the number with x

The required sum can be represented as:

$x + \frac{1}{x}$

Hence, the objective function is:

$S(x) = x + \frac{1}{x}$

To get the the interval, we start by differentiating w.r.t x

<em>Using first principle, this gives:</em>

$S'(x) = 1 - \frac{1}{x^2}$

Equate S'(x) to 0 in order to solve for x

$0 = 1 - \frac{1}{x^2}$

Subtract 1 from both sides

$0 -1 = 1 -1 - \frac{1}{x^2}$

$-1 = - \frac{1}{x^2}$

Multiply both sides by -1

$1 = \frac{1}{x^2}$

Cross Multiply

$x^2 * 1 = 1$

$x^2 = 1$

Take positive square root of both sides because x is positive

$\sqrt{x^2} = \sqrt{1$

$x = 1$

Representing x using interval notation, we have

Interval = $\{x:x=1\}$

To get the smallest sum, we substitute 1 for x in $S(x) = x + \frac{1}{x}$

$S(1) = 1 + \frac{1}{1}$

$S(1) = 1 + 1$

$S(1) = 2$

<em>Hence, the smallest sum is 2</em>

3 0

3 years ago

Round each addendum to the nearest ten. 478 + 112

Amiraneli [1.4K]

500 and 100 because if you see the seven right, seven is the judge and so as the one. Make it 500 and the next number 100. So you'll have en estimate of 600. Ur welcome.

8 0

3 years ago

One side of a rectangle is 9 millimeters shorter than six times the other side. Find the length of the longer side if we also kn

vodka [1.7K]

Given:

W(width) = (6L) - 9

L(length) = L

Equation:

2( [ 6L ] - 9) + 2 (L) = 150

= 12L - 18 + 2L = 150

= 12L + 2L = 150 + 18

=14L = 168

L = 168/14, so the length is 12. Let's check our work.

Width: 6(12) - 9 = 72 - 9 = 63

Length: 12

Since there are two lines of width and two lines of length:

2(12) + 2(63) = 24 + 126, which gives you a perimeter of 150 mm.

Hope this helped.

4 0

3 years ago

Maria makes beaded necklaces. She charges a rate of $0.75 per inch in length plus $0.25 per bead as shown in the expression, whe

sergiy2304 [10]

16x+60y
16(.75)+60(.25)
12+15=27
maria would charge $27 for this necklace

3 0

3 years ago

Read 2 more answers

A pyramid has a base area of 60.5 cm^2 and a height of 12 cm what is the volume of the pyramid

Elena L [17]

Answer:

242 cm^3

Step-by-step explanation:

Volume of a pyramid = 1/3 * area of base * height

= 1/3 * 60.5 * 12

= 242 cm^3

7 0

3 years ago